# US 2014/0153675 A1 · Estimation of a Time, Phase and Frequency Shift of an OQAM Multicarrier Signal

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- Number: US 2014/0153675 A1
- Document ID: US20140153675A1
- Status: Published application
- Kind: A1
- Application number: 14/129,739
- Filed: 2012-06-28
- Published: 2014-06-05
- Earliest claimed: 2011-06-30
- Assignees: Orange
- Inventors: Youssef Dandach; Pierre Siohan
- Web page: https://patentgrep.com/patent/US20140153675A1

## CPC

- H04L 27/2654: {Filtering per subcarrier, e.g. filterbank multicarrier [FBMC]}
- H04L 27/2631: {with polyphase implementation}
- H04L 27/2684: {Complexity}
- H04L 27/2698: {double density OFDM/OQAM system, e.g. OFDM/OQAM-IOTA system}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

A method is provided for receiving an OQAM multi-carrier signal, which implements a step of estimating, in the time domain, at least one time, phase, and/or frequency shift of the multi-carrier signal. The estimation step implements at least one estimator in order to estimate the time shift, referred to as a time estimator, and/or at least one estimator for estimating the phase shift, referred to as a phase estimator, and/or at least one estimator for estimating the frequency shift, referred to as a frequency estimator. The multi-carrier signal includes at least one preamble, and at least one of the estimators takes into account coefficients of a prototype filter used in transmission in order to shape at least one preamble inserted into the multi-carrier signal.

## Claims

### Claim 1

A method for receiving an OQAM type multicarrier signal comprising:
estimating, in the time domain, at least one time, phase and/or frequency shift of said multicarrier signal,
said estimating implementing at least one estimator configured to estimate said time shift, called a time estimator, and/or at least one estimator configured to estimate said phase shift, called a phase estimator, and/or at least one estimator configured to estimate said frequency shift, called a frequency estimator,
wherein at least one of said estimators takes account of coefficients of a prototype filter used at transmission to shape at least one preamble inserted into said multicarrier signal.

### Claim 2 (depends on 1)

The method for receiving according to claim 1, wherein at least one of said estimators implements a pseudo-periodicity taking account of said preamble and of said prototype filter.

### Claim 3 (depends on 1)

The method for receiving according to claim 1, wherein estimating implements, in the time domain, a first sub-step of estimating a time shift followed by a second sub-step of estimating a phase shift or a second sub-step of estimating a frequency shift.

### Claim 4 (depends on 3)

The method for receiving according to claim 3, wherein said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


∑
k
=
0
M
/
4
-
1

h

(
k
)

h
(

M
/
2
-
1
-
k
)

r

(
k
+
τ
~
)

r
(

M
/
2
-
1
-
k
+
τ
~
)



and
τ
^
LS
2
=
arg


max
τ
~


∑
k
=
0
M
/
4
-
1

h
(

M
-
1
-
k
)

h
(

M
/
2
+
k
)

r

(
M
/
2
+
k
+
τ
~
)

r

(
M
-
1
-
k
+
τ
~
)

and/or said phase estimator implements said second sub-step of estimating a phase shift according to one of the following equations:
φ
^
LS
1
=
1
2

∠

{
∑
k
=
0
M
/
4
-
1

h

(
k
)

h
(

M
/
2
-
1
-
k
)

r

(
k
+
τ
^
)

r
(

M
/
2
-
1
-
k
+
τ
^
)
}


and
φ
^
LS
2
=
1
2

∠

{
∑
k
=
0
M
/
4
-
1

h
(

M
-
1
-
k
)

h
(

M
/
2
+
k
)

r

(
M
/
2
+
k
+
τ
^
)

r

(
M
-
1
-
k
+
τ
^
)
}
with:
{circumflex over (τ)}LS1 or {circumflex over (τ)}LS2 the estimation of said time shift at output of said time estimator, and
{circumflex over (τ)} the estimation of the time shift fixed at input of the phase shift estimator;
{circumflex over (φ)}LS1 or {circumflex over (φ)}LS2 the estimation of said phase shift at output of said phase estimator;
∠{.} the argument of a complex number;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
k an integer such that 0≦k≦M/4−1;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a maximum predetermined value of {tilde over (τ)};
h(k) coefficients of said prototype filter used at transmission;
r(k) a received multicarrier signal such that r(k)=s(k−τ)ejφ+b(k);
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ said time shift of the received multicarrier signal relative to said sent multicarrier signal;
φ said phase shift of the received multicarrier signal relative to said sent multicarrier signal.

### Claim 5 (depends on 3)

The method for receiving according to claim 3, wherein estimating also takes account of a position of at least one pair of maximum values obtained at transmission for said multicarrier signal,
said position being defined relative to the outputs of a step of transformation, from the frequency domain into the time domain, of a set of data symbols forming said preamble, called preamble symbols.

### Claim 6 (depends on 5)

The method for receiving according to claim 5, wherein, for preamble symbols pm,n defined at input of said step of transforming from the frequency domain to the time domain implemented, at transmission, by:
{
p
m
,
n
=
2
/
2


for


m
=
4

p


and


m
=
1
+
4

p
p
m
,
n
=
-
2
/
2


for


m
=
2
+
4

p


and


m
=
3
+
4

p


and
with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n, p an integer, and 0≦m≦M−1,
said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


r

(
τ
~
)

r
(

M
/
2
-
1
+
τ
~
)

,

τ
^
LS
2
=
arg


max
τ
~


r
(

M
/
2
+
τ
~
)

r

(
M
-
1
+
τ
~
)

,
with:
{circumflex over (τ)}LS1 or {circumflex over (τ)}LS2 the estimation of said time shift at output of said time estimator;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)};
r(k) a received multicarrier signal such that r(k)=s(k−τ)ejφ+b(k);
k an integer,
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ a time shift of the received multicarrier signal relative to the sent multicarrier signal;
φ a phase shift of the received multicarrier signal relative to the sent multicarrier signal.

### Claim 7 (depends on 5)

The method for receiving according to claim 5, wherein for preamble symbols pm,n defined at input of said step of transformation from the frequency domain to the time domain implemented at transmission by:
{
p
2

m
,
n
=
2
/
2
p
2

m
+
1
,
n
=
j


2
/
2

for


0
≤
m
≤
M
/
2
-
1
with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n, and j2=−1,
said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


r

(
M
/
4
-
1
+
τ
~
)

r

(
M
/
4
+
τ
~
)

,

τ
^
LS
2
=
arg


max
τ
~


r

(
3

M
/
4
-
1
+
τ
~
)

r

(
3

M
/
4
+
τ
~
)

,
with:
{circumflex over (τ)}LS1 or {circumflex over (τ)}LS2 the estimation of said time shift at output of said time estimator;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)} with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)},
r(k) a received multicarrier signal such that r(k)=s(k−τ)ejφ+b(k);
k an integer;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ a time shift of the received multicarrier signal relative to the sent multicarrier signal;
φ a phase shift of the received multicarrier signal relative to the sent multicarrier signal.

### Claim 8 (depends on 5)

The method for receiving according to claim 5, wherein, for preamble symbols pm,n defined at input of the step of transformation from the frequency domain to the time domain implemented at transmission by: *
{
p
2

m
,
n
=
2
/
2
p
2

m
+
1
,
n
=
0

for


0
≤
m
≤
M
/
2
-
1
with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n, said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


r

(
M
/
4
-
1
+
τ
~
)

r

(
M
/
4
+
τ
~
)

,

τ
^
LS
2
=
arg


max
τ
~


r

(
3

M
/
4
-
1
+
τ
~
)

r

(
3

M
/
4
+
τ
~
)

,
τ
^
LS
3
=
arg


max
τ
~


r

(
M
/
4
-
1
+
τ
~
)

r

(
3

M
/
4
+
τ
~
)
+
r

(
M
/
4
+
τ
~
)

r

(
3

M
/
4
-
1
+
τ
~
)

,
with:
{circumflex over (τ)}LS1, {circumflex over (τ)}LS2 or {circumflex over (τ)}LS3 the estimation of said time shift at output of said time estimator;
M is the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{circumflex over (τ)} is an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)};
r(k) a received multicarrier signal such that r(k)=s(k−τ)ejφ+b(k);
k an integer;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ a time shift of the received multicarrier signal relative to the sent multicarrier signal;
φ a phase shift of the received multicarrier signal relative to the received multicarrier signal.

### Claim 9 (depends on 5)

The method for receiving according to claim 5, wherein, for preamble symbols pm,n defined at the input of the step of transformation from the frequency domain to the time domain implemented at transmission by:
{
p
2

m
,
n
=
(
-
1
)
m

2
/
2
p
2

m
+
1
,
n
=
0

for


0
≤
m
≤
M
/
2
-
1
with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


r

(
τ
~
)

r

(
M
/
2
-
1
+
τ
~
)

,

τ
^
LS
2
=
arg


max
τ
~


r

(
M
/
2
+
τ
~
)

r

(
M
-
1
+
τ
~
)

,

τ
^
LS
3
=
arg


max
τ
~


r

(
τ
~
)

r

(
M
-
1
+
τ
~
)
+
r

(
M
/
2
-
1
+
τ
~
)

r

(
M
/
2
+
τ
~
)

,
with:
{circumflex over (τ)}LS1, {circumflex over (τ)}LS2 or {circumflex over (τ)}LS3 the estimation of said time shift at output of said time estimator;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)};
r(k) a received multicarrier signal, such that r(k)=s(k−τ)ejφ+b(k);
k an integer;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ a time shift of the received multicarrier signal relative to the sent multicarrier signal;
φ a phase shift of the received multicarrier signal relative to the sent multicarrier signal.

### Claim 10 (depends on 5)

The method for receiving according to claim 5, wherein for preamble symbols pm,n defined at input of the first step of transformation from the frequency domain to the time domain implemented, at transmission, by:
{
p
m
,
n
=
1
if


mod

(
m
,
4
)
=
0
p
m
,
n
=
0
else

for


0
≤
m
≤
m
-
1
with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n, said time estimator implements said first sub-step of estimating a time shift according to one of the following equations:
τ
^
LS
1
=
arg


max
τ
~


r

(
τ
~
)

r

(
M
/
2
-
1
+
τ
~
)
+
r

(
M
/
4
-
1
+
τ
~
)

r

(
M
/
4
+
τ
~
)

τ
^
LS
2
=
arg


max
τ
~


r

(
M
/
2
+
τ
~
)

r

(
M
-
1
+
τ
~
)
+
r

(
3

M
/
4
-
1
+
τ
~
)

r

(
3

M
/
4
+
τ
~
)

τ
^
LS
3
=
arg


max
τ
~


r

(
τ
~
)

r

(
M
-
1
+
τ
~
)
+
r

(
M
/
4
-
1
+
τ
~
)

r

(
3

M
/
4
+
τ
~
)
+
r

(
M
/
4
+
τ
~
)

r

(
3

M
/
4
-
1
+
τ
~
)
+
r

(
M
/
2
-
1
+
τ
~
)

r

(
M
/
2
+
τ
~
)

with:
{circumflex over (τ)}LS1, {circumflex over (τ)}LS2 or {circumflex over (τ)}LS3 the estimation of said time shift at output of said time estimator;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)};
r(k) a received multicarrier signal such that r(k)=s(k−τ)ejφ+b(k);
k an integer;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ a time shift of the received multicarrier signal relative to the sent multicarrier signal;
φ a phase shift of the received multicarrier signal relative to the sent multicarrier signal.

### Claim 11 (depends on 3)

The method for receiving according to claim 3, wherein estimating takes account of the fact that at least one of the preamble symbols appreciably comprises one in every two sub-carriers having a zero value.

### Claim 12 (depends on 11)

The method for receiving according to claim 11, wherein, for preamble symbols pm,n, defined at input to said step of transformation from the frequency domain to the time domain, the first symbol sent at the instant n=0 such that:
{
p
2

m
,
0
=
d


with


d
∈



or


d
∈

P
2

m
+
1
,
0
=
0

or

{
P
2

m
,
0
=
0
p
2

m
+
1
,
0
=
d


with


d
∈



or


d
∈

with pm,n a preamble symbol associated with a sub-carrier with index m at the instant n=0, and 0≦m≦M/2−1, with M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
while the following signal sent at the instant n=1 corresponds to a zero symbol such that:
pm,1=0, for 0≦m≦M−1
said time estimator implements said first sub-step of estimation of a time shift according to the following equation:
τ
^
LS
=
arg


max
τ
~

{
2


R
1

(
τ
~
)

-
Q
1

(
τ
~
)
}
,
and said frequency estimator implements said second sub-step of estimating a frequency shift according to the following equation:
Δ


f
^
LS
=
1
π


N

arg


{
R
1

(
τ
~
LS
)
}
,

with

:
R
1

(
τ
~
)
=
∑
k
=
0
M
/
2
-
1

h

(
k
)

h

(
k
+
M
/
2
)

r
*
(
k
+
τ
~
)

r

(
k
+
M
/
2
+
τ
~
)
,

Q
1

(
τ
~
)
=
∑
k
=
0
M
/
2
-
1

h

(
k
)
2


r

(
k
+
τ
~
)

2
+
h

(
k
+
M
/
2
)
2


r

(
k
+
M
/
2
+
τ
~
)

2
,
τLS the estimation of the time shift at output from the time estimator;
Δ{circumflex over (f)}LS the estimation of said frequency shift at output from the phase estimator;
M the number of sub-carriers of an OQAM signal of the multicarrier signal;
k an integer such that 0≦k≦M/2−1;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)}
h(k) coefficients of said prototype filter used at transmission;
r(k) a received multicarrier signal such that r(k)=ej2πΔf [c(k)s(k−τ)]+b(k); (k)
a product of convolution;
c(k) the response of a multipath channel;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ said time shift of the received multicarrier signal relative to the sent multicarrier signal;
Δf said frequency shift of the received multicarrier signal relative to the sent multicarrier signal.

### Claim 13 (depends on 11)

The method for receiving according to claim 11, wherein, for preamble symbols pm,n, defined at input of said step of transformation from the frequency domain to the time domain, the first symbol sent at the instant n=0 is such that:
{
p
2

m
,
0
=
d


with


d
∈



or


d
∈

P
2

m
+
1
,
0
=
0

or

{
P
2

m
,
0
=
0
p
2

m
+
1
,
0
=
d


with


d
∈



or


d
∈

with pm,n a preamble symbol associated with a sub-carrier of index m at the instant n=0, and 0≦m≦M/2−1, M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
while the next symbol sent at the instant n=1 corresponds to a zero symbol such that:
pm,1=0, for 0≦m≦M−1
and wherein estimating takes account also of the position of at least a pair of maximum values obtained at transmission for said multicarrier signal,
said position being defined relative to the outputs of a step of transformation, from the frequency domain to the time domain (12), of a set of data symbols intended to form said preamble, called preamble symbols,
said time estimator implements said first sub-step of estimating a time shift according to the following equation:
τ
^
LS
=
arg


max
τ
~

{

R
1

(
τ
~
)


Q
1

(
τ
~
)
}
,
and said frequency estimator implements said second step of estimating a frequency shift according to the following equation:
Δ


f
^
LS
=
1
2

π


N

arg


{
R
1

(
τ
~
LS
)
}
,
with k an integer, M the number of sub-carriers of an OQAM symbol of said multicarrier signal, and said positions of maximum values following k, M/2−1−k, M/2+k, M−1−k:
R({circumflex over (τ)})=h(k)h(k+M/2)r*(k+{tilde over (τ)})r(k+M/2+{tilde over (τ)})+h(M/2−1−k)h(M−1−k)r*(M/2−1−k+{tilde over (τ)})r(M−1−k+{tilde over (τ)})
Q({tilde over (τ)})=h(k+M/2)2|r(k+{tilde over (τ)})|2+h(M−1−k)2|r(M/2−1−k+{tilde over (τ)})|2+h(k)|r(M/2+k+{tilde over (τ)})|2h(M/2−1−k)2|r(M−1−k+{tilde over (τ)})|2,
{circumflex over (τ)}LS the estimation of said time shift at output of said time estimator;
ΔfLS the estimation of said frequency shift at output of said phase estimator;
M the number of sub-carriers of an OQAM symbol of said multicarrier signal;
{tilde over (τ)} an integer such that 0≦{tilde over (τ)}≦{tilde over (τ)}max with {tilde over (τ)}max a predetermined maximum value of {tilde over (τ)}
h(k) coefficients of said prototype filter used at transmission;
r(k) a received multicarrier signal such that r(k)=ej2πΔf [c(k)s(k−τ)]+b(k);
a product of convolution;
c(k) the response of a multipath channel;
s(k) a sent multicarrier signal;
b(k) a Gaussian white noise;
τ said time shift of the received multicarrier signal relative to said sent multicarrier signal;
Of said frequency shift of the received signal relative to said sent multicarrier signal.

### Claim 14

A device for receiving an OQAM type multicarrier signal comprising:
means for estimating, in the time domain, at least one timing, phase and/or frequency shift of said multicarrier signal,
said means for estimating comprising at least one estimator for estimation of the time shift, called a time estimator, and/or at least one estimator for estimating the phase shift, called a phase estimator, and/or at least one estimator for estimating the frequency shift, called a frequency estimator,
wherein at least one of said estimators takes account of efficiency of a prototype filter used at transmission to shape at least one preamble in said multicarrier signal.

### Claim 15

A non-transitory computer readable medium comprising a computer program stored thereon and comprising instructions for implementing a method for receiving an OQAM type multicarrier signal when the program is executed by a processor, wherein the method comprises:
estimating by a receiver device, in the time domain, at least one time, phase and/or frequency shift of said multicarrier signal,
said estimating implementing at least one estimator configured to estimate said time shift, called a time estimator, and/or at least one estimator configured to estimate said phase shift, called a phase estimator, and/or at least one estimator configured to estimate said frequency shift, called a frequency estimator,
wherein at least one of said estimators takes account of coefficients of a prototype filter used at transmission to shape at least one preamble inserted into said multicarrier signal.